🧮 algebra

1. **Problem statement:** Given that $\log 17 = k$, find an expression for $\log 170$.\n\n2. **Recall the logarithm property:** $\log(ab) = \log a + \log b$. This means the logarit

1. **Planteamiento del problema:** Tenemos las matrices $$A=\begin{pmatrix}2 & -1 \\ 3 & 2\end{pmatrix}, \quad B=\begin{pmatrix}0 & 1 \\ 4 & -2\end{pmatrix}$$

1. The problem appears to involve simplifying or manipulating the expression $A^2 - B$. 2. To proceed, we need to clarify the operation or goal, but assuming simplification or fact

1. **State the problem:** Simplify the expression $$\frac{(2xr)^0}{x - 2y^3 - 2xr^3}$$. 2. **Recall the rule:** Any nonzero number or expression raised to the power 0 equals 1, i.e

1. **State the problem:** Simplify the expression $$\left( \frac{2x^3 y^2}{x^3 y^7 x^4} \right)^{-3}$$. 2. **Rewrite the expression inside the parentheses:** Combine like terms in

1. **State the problem:** Solve the equation $$2^{x+4} = 2^{(x+5)3}$$ for $x$. 2. **Recall the property of exponents:** If $$a^m = a^n$$ and $$a > 0, a \neq 1$$, then $$m = n$$.

1. The problem is to express 7% as a fraction and a decimal. 2. Recall that percent means per hundred, so 7% can be written as \(\frac{7}{100}\).

1. **State the problem:** Simplify the expression $4\sqrt{112}$. 2. **Recall the rule:** The square root of a product can be written as the product of square roots: $$\sqrt{a \time

1. El problema es calcular el producto de dos matrices: $A = \begin{pmatrix}4 & 2 \\ 3 & 2\end{pmatrix}$ y $B = \begin{pmatrix}2 & 4 \\ -1 & 2\end{pmatrix}$. Queremos encontrar $(A

1. The problem is to evaluate the expression $6 \div 2(1 + 2)$.\n\n2. According to the order of operations (PEMDAS/BODMAS), we first solve expressions inside parentheses.\n\n3. Cal

1. **State the problem:** Evaluate the expression $$6 \div 2(1 + 2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** We are given a function that models the credit left on a prepaid phone card after making calls. The function is:

1. **State the problem:** We need to find the height of the plant after 20 months given the function $$H(x) = 8.00 + 0.08x$$ where $H(x)$ is the height in meters and $x$ is the num

1. **State the problem:** We want to solve the equation $$2x^2 + 3x = 4$$ using an iterative method and find the solution near $$x = -2$$ correct to 4 significant figures. 2. **Rew

1. **State the problem:** We have a parabolic arch represented by the polynomial $$p(x) = -0.0025x^2 - 0.025x + 136$$. (i) Write the coordinates of point A (the highest point on th

1. **State the problem:** We are given two points on the function $n(x)$: $n(1.36) = 0.9131$ and $n(1.37) = 0.9147$. We want to approximate $n(1.367)$ and $n(1.356)$ using linear i

1. **State the problem:** Solve the system of linear equations: $$\frac{2}{3}x + y = -2$$

1. **Problem:** Find the intersection point of the lines $y=3x+1$ and $y=-x-3$. 2. **Formula and rules:** To find the intersection, set the two equations equal: $$3x+1 = -x-3$$

1. The problem is to understand the shape of the graph of the function $$g(x) = (x + 4)^3 + 3$$. 2. This is a cubic function shifted horizontally and vertically. The base cubic fun

1. **State the problem:** We have the function $g(x) = 6x^2 - 1$.

1. Problemet: Vi har en funktion givet ved $$f(x) = -4x + 5$$ og en tabel med nogle værdier for $x$ og $f(x)$, hvor et tal mangler. Vi skal finde det manglende tal. 2. Formel: Funk